Theory of the magnetic properties of isotropic ladder-type double chains with classical spins at the bunch-upright intersections: Application to Gd(III)-Cu(II) compounds

A general method is proposed for computing the susceptibility of a large category of regular magnetic double chains in which more or less complex quantum spin systems, occupying the uprights and the bunches, are linked through the nodes by magnetic cations. Only two conditions are required: (i) the magnetic cations at the intersections of the uprights and the bunches must exhibit large enough spin quantum numbers to allow a classical treatment and (ii) the overall zero-field Hamiltonian must be isotropic. The main applications of the model are listed. More specifically, results are given for the case where the quantum spin systems are empty, and the neighboring classical spins directly interact through Heisenberg exchange. The model is also used with particular success to interpret the observed magnetic properties of the compound ${\mathrm{Gd}}_2$(ox)[Cu(pba)${]}_3$[Cu(${\mathrm{H}}_2$O${)}_5$]⋅${20\mathrm{H}}_2$O, which enters the general framework, with each quantum system reducing to a single 1/2 spin. It is also applied tentatively to the related compound ${\mathrm{Gd}}_2$[Cu(pba)${]}_3$⋅${23\mathrm{H}}_2$O.